The Boundary Value Problem and the Nonlinear Spatial Dispersion in Collisionless Quark-Gluon Plasma

The boundary value problem of the quark-gluon plasma kinetic equations is analyzed by using the derivative expansion method. The dispersion relation in the linear approximation indicates that there is no collisionless spatial damping, but it reflects that the nonlinear interaction between the eigenwaves in it is very important. By taking account of the nonlinear interactions of waves, the resonance condition between the secondary waves and the particles in quark-gluon plasma can be fulfilled which will result in the spatial damping. The nonlinear spatial collisionless damping rate for the longitudinal secondary color waves in the long wavelength limit has been calculated numerically.